He also suggested the following:
Upon hearing of this, contacting Capcom for comment is just what I did. I was told "we don’t have any plans to further improve the performance of Mega Man 5 in MMLC on 3DS at this time," so it unfortunately seems like fans are stuck with it for now. I'll keep you updated if there is any change.
Fortunately, not all is lost. Word has it that if you switch to Rockman Mode, Rockman 5 runs just fine. The reason one works better than the other is currently unknown. Fortunately -- especially as the Nintendo 3DS version is the only one with a Rockman Mode -- the handheld version appears to be the only one experiencing this issue.